Answer:
x ≈ 5.38 meters
Explanation:
Pre-Solving
We are given a right triangle. We know that the length of the hypotenuse (the side opposite of the right angle) is 25.9 m and one of the legs (the sides that make up the right angle) is x, which is what we want to find.
We also know one of the angles is 78°.
Solving
In order to find the value of x, we need to use trigonometry.
Recall the three trigonometric ratios:
sine, which is
cosine, which is
tangent, which is
These ratios are written in reference to one angle.
We can write our ratios in reference to the 78° angle.
The opposite side will be the other leg (the side that is not labeled), the adjacent side will be the side labeled x, and the hypotenuse will be the side labeled 25.9 m.
Since we have the values of both the adjacent and hypotenuse sides, we can use cosine of 78° to find x.
We set this up as:
cos(78) =
Now, multiply both sides by 25.9
25.9 * cos(78) = x
Plug 25.9 * cos(78) into your calculator. Make sure your calculator is on degree mode.
5.38 ≈ x
So, x is about 5.38 meters.